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Celtics president Danny Ainge has been in talks with David Falk, the representative for restricted free agent forward Jeff Green, who hopes to be on time when training camp begins on Friday.

The Celtics have expressed interest in bringing back Green, who came to Boston as a part of the much-criticized trade that sent center Kendrick Perkins to Oklahoma City at last season’s deadline.

Green is weighing his options, which include a best-case scenario of signing a multiyear deal with Boston, working out a sign-and-trade, or accepting the Celtics’ qualifying offer and waiting to become a free agent next summer.

“Jeff has a desire to be in Boston,’’ Falk said. “Boston has a need. I hope Danny and I can come up with a creative way to reach an agreement.’’

The Celtics extended a $6 million qualifying offer to Green before the lockout. If he accepts it, the Celtics would be unable to trade Green without his permission.

It’s different from the situation that brought Green to Boston. The Celtics couldn’t reach terms on an extension with Perkins and didn’t want to lose him without getting anything in return, so they traded him and guard Nate Robinson to the Thunder for Green and center Nenad Krstic.

The Celtics not reaching a deal with Green, Falk said, would mean getting little for Perkins, ostensibly renting Green for a season and a half.

“Their ability to protect his value depends on his ability to make a multiyear deal,’’ Falk said.

If Green signs a multiyear deal, he’d be a secure piece of the Celtics’ future. But if he accepts the qualifying offer and waits to become a free agent - which isn’t that long of a wait because of the shortened season - he could benefit from being available during an offseason when many teams are expected to have money.

The 6-foot-9-inch, 235-pound Green came to Boston with the expectation that he’d be long and athletic and able to play both forward spots and even some center. But for the first time since he was a kid, he was coming off the bench, and the adjustment was difficult.

He played 26 games (two starts) with Boston, and his numbers dipped. As a starter (49 games) in Oklahoma City, Green averaged 37 minutes, 15.2 points, and 5.6 rebounds. With Boston, his minutes dropped to 23.5 a night, his points to 9.8, and his rebounds to 3.3.

“I think Jeff feels like he has unfinished business in Boston,’’ Falk said. “I’m not sure the people in Boston have seen the real Jeff Green.’’

There are four scenarios.

Green and the Celtics could reach a long- or short term-deal. Green has Larry Bird rights (allowing the Celtics to exceed the cap to re-sign him), so he’s eligible to make up to the maximum of $13.6 million.

Green could accept the qualifying offer. To a player, that’s the equivalent of signing for the minimum, a one-year deal for the least amount the team is required to pay.

The sides could determine that they can’t come to terms, and decide on a sign-and-trade. The Celtics would be able to get something in return for Green, and Green would be able to sign a deal he likes.

Green could sign an offer sheet from another team, which Falk says he won’t do. It would mean the Celtics would get nothing out of the Perkins trade.

Falk has known Ainge and coach Doc Rivers for nearly 30 years, he said, and emphasized that the talks have been “extremely friendly and positive.’’

“The best surprise is no surprise,’’ Falk said. “I don’t think you have to blow up a building to get a deal done. We have a great rapport.’’

The 25-year-old Green’s youth is important, not just because of the condensed 66-game schedule but because of the possibility that by 2013, Ray Allen, Kevin Garnett, and Paul Pierce could all be retired.

“In order for Boston to maintain a good team they have to have three players,’’ Falk reasoned. “[Rajon] Rondo’s one. Green’s two. And they would need another.’’

By not signing Green - or not figuring out a way to trade him for another piece - the Celtics would essentially concede to “blow up the team to start all over again,’’ according to Falk.

“There’s a tremendous pressure to maintain continuity and keep Jeff Green,’’ he said.

Training camp starts Friday, and Falk wants Green to be there.

“I want Jeff in camp on time,’’ Falk said. “I expect to have him in training camp on time, whichever training camp he’s in.’’